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Some Democrats are “Ready for Hillary.” MoveOn.org is ready for Elizabeth Warren.

The liberal group is poised to spend $1 million on a campaign to draft Senator Warren, the Massachusetts Democrat, into the 2016 presidential race, an indication of an appetite among some activists for a more progressive alternative to Hillary Rodham Clinton.

MoveOn.org’s executive director, Ilya Sheyman, said the group planned to open offices and hire staff in Iowa and New Hampshire, the states that kick off the presidential nominating process, and ultimately to air television ads in those states. The group will begin its push with a website, “Run Warren Run,” allowing supporters to sign a petition urging Ms. Warren to pursue a White House bid and featuring a video about her.